Implementation of Soft and Hard Threshold Denoising Codes along with a Novel Threshold Function Denoising Code

We provide comprehensive implementations of soft and hard threshold denoising algorithms, established signal processing techniques for effective noise reduction in various signal types. The soft threshold method applies continuous shrinkage to signal coefficients exceeding the threshold, while the hard threshold approach completely zeroes out coefficients below the threshold. Additionally, we offer a novel threshold function denoising implementation that employs an advanced mathematical formulation for more precise noise detection and elimination. This innovative approach enhances signal quality through improved threshold selection mechanisms and adaptive coefficient handling. These algorithms are implemented with optimized computational efficiency and can be effectively applied across multiple domains including digital image processing (for removing Gaussian noise), audio signal enhancement (reducing background interference), and communication systems (improving signal-to-noise ratio in transmission channels). The code includes parameter optimization functions and visualization tools for performance evaluation.